Exploració per autor "Fedorov, Yuri"
Ara es mostren els items 7-21 de 21
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Closed Geodesics and Billiards on Quadrics related to elliptic KdV solutions
Abenda, Simonetta; Fedorov, Yuri (2004)
Article
Accés obertWe consider algebraic geometrical properties of the integrable billiard on a quadric Q with elastic impacts along another quadric confocal to Q. These properties are in sharp contrast with those of the ellipsoidal Birkho® ... -
Continuous and discrete neumann systems on stiefel varieties as matrix generalizations of the jacobi-mumford systems
Fedorov, Yuri; Jovanovic, Božidar (2021-06-01)
Article
Accés obertWe study geometric and algebraic geometric properties of the continuous and discrete Neumann systems on cotangent bundles of Stiefel varieties Vn,r. The systems are integrable in the non-commutative sense, and by applying ... -
Discrete nonholonomic LL systems on Lie groups
Fedorov, Yuri; Zenkov, Dmitry (2003)
Article
Accés obertThis paper applies the recently developed theory of discrete nonholonomic mechanics to the study of discrete nonholonomic left-invariant dynamics on Lie groups. The theory is illustrated with the discrete versions of two ... -
Geodesic flows and Neumann systems on Stiefel varieties: geometry and integrability
Fedorov, Yuri (2010-12-03)
Article
Accés restringit per política de l'editorialWe study integrable geodesic flows on Stiefel varieties Vn,r = SO(n)/SO(n−r ) given by the Euclidean, normal (standard), Manakov-type, and Einstein metrics.We also consider natural generalizations of the Neumann systems ... -
Homoclinic billiard orbits inside symmetrically perturbed ellipsoids
Delshams Valdés, Amadeu; Fedorov, Yuri; Ramírez Ros, Rafael (2000)
Article
Accés obertThe billiard motion inside an ellipsoid of ${\bf R}^{3}$ is completely integrable. If the ellipsoid is not of revolution, there are many orbits bi-asymptotic to its major axis. The set of bi-asymptotic orbits is described ... -
Integrable nonholonomic geodesic flows on compact Lie groups
Fedorov, Yuri; Jovanovic, Bozidar D. (2003)
Article
Accés obertThis paper is a review of recent results on integrable nonholonomic geodesic flows of left–invariant metrics and left- and right–invariant constraint distributions on compact Lie groups. -
Nonholonomic LR systems as Generalized Chaplygin systems with an invariant measure and geodesic flows on homogeneous spaces
Fedorov, Yuri; Jovanovic, Bozidar D. (2003)
Article
Accés obertWe consider a class of dynamical systems on a compact Lie group G with a left-invariant metric and right-invariant nonholonomic constraints (so called LR systems) and show that, under a generic condition on the constraints, ... -
On the construction of elliptic solutions of integrable birational maps
Petrera, Matteo; Pfadler, Andreas; Suris, Yuri B.; Fedorov, Yuri (2017-01-01)
Article
Accés obertWe present a systematic technique to find explicit solutions of birational maps, provided that these solutions are given in terms of elliptic functions. The two main ingredients are the following: (i) application of classical ... -
Separation of variables and explicit theta-function solution of the classical Steklov--Lyapunov systems: A geometric and algebraic geometric background
Fedorov, Yuri; Basak Gancheva, Inna (2009-11)
Report de recerca
Accés obertAbstract The paper revises the separation of variables and explicit integration of the classical Steklov{ Lyapunov systems, which was ¯rst made by F. KÄotter in 1900. Namely, we give a geometric interpretation of the ... -
Sigma-function solution to the general Somos-6 recurrence via hyperelliptic Prym varieties
Fedorov, Yuri; Hone, Andy (Oxford University Press, 2016-09-09)
Article
Accés obertWe construct the explicit solution of the initial value problem for sequences generated by the general Somos-6 recurrence relation, in terms of the Kleinian sigma-function of genus 2. For each sequence there is an associated ... -
Steklov-Lyapunov type systems
Bolsinov, A. V.; Fedorov, Yuri (2003)
Article
Accés obertIn this paper we describe integrable generalizations of the classical Steklov– Lyapunov systems, which are defined on a certain product so(m) × so(m), as well as the structure of rank r coadjoint orbits in so(m)×so(m). ... -
The hydrodynamic Chaplygin sleigh
Fedorov, Yuri; García Naranjo Ortiz de la Huerta, Luis Constantino (2010)
Article
Accés obertWe consider the motion of rigid bodies in a potential fluid subject to certain nonholonomic constraints and show that it is described by Euler–Poincar´e– Suslov equations. In the two-dimensional case, when the constraint ... -
The motion of the 2D hydrodynamic chaplygin sleigh in the presence of circulation
Fedorov, Yuri; García Naranjo, Luis C.; Vankerschaver, Joris (2013-03)
Article
Accés obertWe consider the motion of a planar rigid body in a potential two-dimensional flow with a circulation and subject to a certain nonholonomic constraint. This model can be related to the design of underwater vehicles. ... -
The Picard-Fuchs equations for complete hyperelliptic integrals of even order curves, and the actions of the generalized Neumann system
Fedorov, Yuri; Pantazi, Chara (2014-03-01)
Article
Accés obertWe consider a family of genus 2 hyperelliptic curves of even order and obtain explicitly the systems of 5 linear ordinary differential equations for periods of the corresponding Abelian integrals of first, second, and third ... -
The sigma function over a family of curves with a singular fiber
Fedorov, Yuri; Komeda, Jiyro; Matsutani, Shigeki; Previato, Emma; Aomoto, Kazuhiko (2022-01-01)
Article
Accés restringit per política de l'editorialIn this paper we investigate the behavior of the sigma function over the family of cyclic trigonal curves Xs defined by the equation y3=x(x-s)(x-b1)(x-b2) in the affine (x, y) plane, for s ¿ De:= {s ¿ C¿s| < e}. We compare ...